Z Confidence Interval for Means – Example

Calculate a 95% C.I. on the mean for a sample (n = 35) with an x-bar of 15.6″and a known s of 2.3 ”

This interval represents the most likely distribution of population means, given the sample’s size, mean, and the population’s standard deviation. 95% of the time, the population’s mean will fall in this interval.

Use the t distribution for the confidence interval for a mean if the sample size n is relatively small (< 30), and/or s is not known. The confidence interval (C.I.) includes the shaded area under the curve in between the critical values, excluding the tail areas (the a risk). The entire curve represents the most likely distribution of population means, given the sample’s size, mean, and standard deviation.

Use the χ2 (chi-squared) distribution for the confidence interval for the variance The confidence interval (C.I.) includes the area under the curve in between the critical values, excluding the tail areas (the a risk). The entire curve represents the most likely distribution of population variances (sigma squared), given the sample’s size and variation.

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